How long does a site, like Law beta, stay in the beta stage before becoming a permanent site? Is it a timeframe benchmark or a user benchmark?
If this information is in a specific area, can you please add a link.
Good question! This was actually addressed by Stack Exchange a few months ago.
If you want to get a sense of how the site is doing you can always check in on its Area51 stats. (However, as one commentator noted, "Even the SE team has repeatedly emphasized that the current A51 stats do not matter as to whether a site will be graduated, as there are far more important (and subjective) goals, such as sense of community, self-moderation, user retention, etc....")
For such a young beta Law is (currently) doing extraordinarily well.